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# Mathematics

## Core Competencies

### Big Ideas

### Grandes idées

Fractions and decimals are types of numbers that can represent quantities.

numbers

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- What is the relationship between fractions and decimals?
- How are these fractions (e.g., 1/2 and 7/8) alike and different?
- How do we use fractions and decimals in our daily life?
- What stories live in numbers?
- How do numbers help us communicate and think about place?
- How do numbers help us communicate and think about ourselves?

Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.

fluency

- Computational Fluency: Computational fluency develops from a strong sense of number.
*Sample questions to support inquiry with students:*- What is the relationship between multiplication and division?
- What patterns in our number system connect to our understanding of multiplication?
- How does fluency with basic multiplication facts (e.g., 2x, 3x, 5x) help us compute more complex multiplication facts?

Regular changes in patterns can be identified and represented using tools and tables.

patterns

- Patterning: We use patterns to represent identified regularities and to make generalizations.
- Sample questions to support inquiry with students:
- What regularities can you identify in these patterns?
- Where do we see patterns in the world around us?
- How can we represent increasing and decreasing regularities that we see in number patterns?
- How do tables and charts help us understand number patterns?

Polygons are closed shapes with similar attributes that can be described, measured, and compared.

attributes

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- How are these polygons alike and different?
- How can we measure polygons?
- How do the properties of shapes contribute to buildings and design?

Analyzing and interpreting experiments in data probability develops an understanding of chance.

data

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
*Sample questions to support inquiry with students:*- How is the probability of an event determined and described?
- What events in our lives are left to chance?
- How do probability experiments help us understand chance?

## Learning Standards

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### Curricular Competencies

*Students are expected to be able to do the following:*### Reasoning and analyzing

Use reasoning to explore and make connections

Estimate reasonably

Estimate reasonably

- estimating by comparing to something familiar (e.g., more than 5, taller than me)

Develop mental math strategies and abilities to make sense of quantities

mental math strategies

- working toward developing fluent and flexible thinking about number

Use technology to explore mathematics

technology

- calculators, virtual manipulatives, concept-based apps

Model mathematics in contextualized experiences

Model

- acting it out, using concrete materials, drawing pictures

### Understanding and solving

Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Visualize to explore mathematical concepts

Develop and use multiple strategies to engage in problem solving

multiple strategies

- visual, oral, play, experimental, written, symbolic

Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

connected

- in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration
- Have students pose and solve problems or ask questions connected to place, stories, and cultural practices.

### Communicating and representing

Communicate mathematical thinking in many ways

Communicate

- concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas
- using technology such as screencasting apps, digital photos

Use mathematical vocabulary and language to contribute to mathematical discussions

Explain and justify mathematical ideas and decisions

Explain and justify

- using mathematical arguments
- “Prove it!”

Represent mathematical ideas in concrete, pictorial, and symbolic forms

concrete, pictorial, and symbolic forms

- Use local materials gathered outside for concrete and pictorial representations.

### Connecting and reflecting

Reflect on mathematical thinking

Reflect

- sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions

Connect mathematical concepts to each other and to other areas and personal interests

other areas and personal interests

- to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, the environment, popular media and news events, social justice, and cross-curricular integration)

Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

Incorporate

- Invite local First Peoples Elders and knowledge keepers to share their knowledge.

make connections

- Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining (csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)
- aboriginaleducation.ca
*Teaching Mathematics in a First Nations Context,*FNESC fnesc.ca/k-7/

### Content

*Students are expected to know the following:*number concepts to 10 000

number concepts

- counting:
- multiples
- flexible counting strategies
- whole number benchmarks

- Numbers to 10 000 can be arranged and recognized:
- comparing and ordering numbers
- estimating large quantities

- place value:
- 1000s, 100s, 10s, and 1s
- understanding the relationship between digit places and their value, to 10 000

decimals to hundredths

decimals to hundredths

- Fractions and decimals are numbers that represent an amount or quantity.
- Fractions and decimals can represent parts of a region, set, or linear model.
- Fractional parts and decimals are equal shares or equal-sized portions of a whole or unit.
- understanding the relationship between fractions and decimals

ordering and comparing fractions

fractions

- comparing and ordering of fractions with common denominators
- estimating fractions with benchmarks (e.g., zero, half, whole)
- using concrete and visual models
- equal partitioning

addition and subtraction to 10 000

addition and subtraction

- using flexible computation strategies, involving taking apart (e.g., decomposing using friendly numbers and compensating) and combining numbers in a variety of ways, regrouping
- estimating sums and differences to 10 000
- using addition and subtraction in real-life contexts and problem-based situations
- whole-class number talks

multiplication and division of two- or three-digit numbers by one-digit numbers

multiplication and division

- understanding the relationships between multiplication and division, multiplication and addition, division and subtraction
- using flexible computation strategies (e.g., decomposing, distributive principle, commutative principle, repeated addition and repeated subtraction)
- using multiplication and division in real-life contexts and problem-based situations
- whole-class number talks

addition and subtraction of decimals to hundredths

decimals

- estimating decimal sums and differences
- using visual models, such as base 10 blocks, place-value mats, grid paper, and number lines
- using addition and subtraction in real-life contexts and problem-based situations
- whole-class number talks

addition and subtraction facts to 20 (developing computational fluency)

computational fluency

- Provide opportunities for authentic practice, building on previous grade-level addition and subtraction facts.
- flexible use of mental math strategies

multiplication and division facts to 100 (introductory computational strategies)

facts

- Provide opportunities for concrete and pictorial representations of multiplication.
- building computational fluency
- Use games to provide opportunities for authentic practice of multiplication computations.
- looking for patterns in numbers, such as in a hundred chart, to further develop understanding of multiplication computation
- Connect multiplication to skip-counting.
- Connecting multiplication to division and repeated addition.
- Memorization of facts is not intended for this level.
- Students will become more fluent with these facts.
- using mental math strategies, such as doubling or halving
- Students should be able to recall the following multiplication facts by the end of Grade 4 (2s, 5s, 10s).

increasing and decreasing patterns, using tables and charts

patterns

- Change in patterns can be represented in charts, graphs, and tables.
- using words and numbers to describe increasing and decreasing patterns
- fish stocks in lakes, life expectancies

algebraic relationships among quantities

algebraic relationships

- representing and explaining one-step equations with an unknown number
- describing pattern rules, using words and numbers from concrete and pictorial representations
- planning a camping or hiking trip; planning for quantities and materials needed per individual and group over time

one-step equations with an unknown number, using all operations

one-step equations

- one-step equations for all operations involving an unknown number (e.g., ___ + 4 = 15, 15 – □ = 11)
- start unknown (e.g., n + 15 = 20; 20 – 15 = □)
- change unknown (e.g., 12 + n = 20)
- result unknown (e.g., 6 + 13 = __)

how to tell time with analog and digital clocks, using 12- and 24-hour clocks

tell time

- understanding how to tell time with analog and digital clocks, using 12- and 24-hour clocks
- understanding the concept of a.m. and p.m.
- understanding the number of minutes in an hour
- understanding the concepts of using a circle and of using fractions in telling time (e.g., half past, quarter to)
- telling time in five-minute intervals
- telling time to the nearest minute
- First Peoples use of numbers in time and seasons, represented by seasonal cycles and moon cycles (e.g., how position of sun, moon, and stars is used to determine times for traditional activities, navigation)

regular and irregular polygons

polygons

- describing and sorting regular and irregular polygons based on multiple attributes
- investigating polygons (polygons are closed shapes with similar attributes)
- Yup’ik border patterns

perimeter of regular and irregular shapes

perimeter

- using geoboards and grids to create, represent, measure, and calculate perimeter

line symmetry

line symmetry

- using concrete materials such as pattern blocks to create designs that have a mirror image within them
- First Peoples art, borders, birchbark biting, canoe building
- Visit a structure designed by First Peoples in the local community and have the students examine the symmetry, balance, and patterns within the structure, then replicate simple models of the architecture focusing on the patterns they noted in the original.

one-to-one correspondence and many-to-one correspondence, using bar graphs and pictographs

one-to-one correspondence

- many-to-one correspondence: one symbol represents a group or value (e.g., on a bar graph, one square may represent five cookies)

probability experiments

probability experiments

- predicting single outcomes (e.g., when you spin using one spinner and it lands on a single colour)
- using spinners, rolling dice, pulling objects out of a bag
- recording results using tallies
- Dene/Kaska hand games, Lahal stick games

financial literacy — monetary calculations, including making change with amounts to 100 dollars and making simple financial decisions

financial literacy

- making monetary calculations, including decimal notation in real-life contexts and problem-based situations
- applying a variety of strategies, such as counting up, counting back, and decomposing, to calculate totals and make change
- making simple financial decisions involving earning, spending, saving, and giving
- equitable trade rules

**Note:**Some of the learning standards in the PHE curriculum address topics that some students and their parents or guardians may feel more comfortable addressing at home. Refer to ministry policy regarding opting for alternative delivery.